 | Point-nucleon densities of $^{16}$O and $^{20}$Ne obtained from particle-number-projected Hartree-Fock-Bogoliubov states with deformations constrained to the predictions of the \textit{ab initio} PGCM framework. The background plots show slices of the densities through the origin. The black dots and lines show the centers and boundaries of the regions used in the clustered sampling method (see text and SM for details)\@. |
 | Point-nucleon densities of $^{16}$O and $^{20}$Ne obtained from particle-number-projected Hartree-Fock-Bogoliubov states with deformations constrained to the predictions of the \textit{ab initio} PGCM framework. The background plots show slices of the densities through the origin. The black dots and lines show the centers and boundaries of the regions used in the clustered sampling method (see text and SM for details)\@. |
 | The deformed shape of $^{20}$Ne impacts the hydrodynamic flow of its collisions as compared to \oooo{} collisions. Here we show results for charged particle multiplicity $dN_\text{ch}/d\eta$ (top left), mean transverse momentum $\langle p_T\rangle$ (top middle), relative fluctuations of transverse momentum $\delta p_T/\langle p_T\rangle$ (top right), elliptic flow $v_2\{2,|\Delta\eta|>1\}$ (bottom left), triangular flow $v_3\{2,|\Delta\eta|>1\}$ (bottom middle) and the Pearson correlation coefficient $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (bottom right)\@. In each panel, we show the \oooo{} and \nene{} results, as well as their ratio, using both PGCM and NLEFT as nuclear structure inputs. For $\rho(v_2\{2\}^2,\langle p_T\rangle)$ a difference is taken instead of a ratio in the lower panel. We show statistical uncertainties (error bars), the total systematic uncertainty (solid bands) as well as its components being \emph{Trajectum} (hatched) and nuclear structure (dotted)\@. |
 | The deformed shape of $^{20}$Ne impacts the hydrodynamic flow of its collisions as compared to \oooo{} collisions. Here we show results for charged particle multiplicity $dN_\text{ch}/d\eta$ (top left), mean transverse momentum $\langle p_T\rangle$ (top middle), relative fluctuations of transverse momentum $\delta p_T/\langle p_T\rangle$ (top right), elliptic flow $v_2\{2,|\Delta\eta|>1\}$ (bottom left), triangular flow $v_3\{2,|\Delta\eta|>1\}$ (bottom middle) and the Pearson correlation coefficient $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (bottom right)\@. In each panel, we show the \oooo{} and \nene{} results, as well as their ratio, using both PGCM and NLEFT as nuclear structure inputs. For $\rho(v_2\{2\}^2,\langle p_T\rangle)$ a difference is taken instead of a ratio in the lower panel. We show statistical uncertainties (error bars), the total systematic uncertainty (solid bands) as well as its components being \emph{Trajectum} (hatched) and nuclear structure (dotted)\@. |
 | The deformed shape of $^{20}$Ne impacts the hydrodynamic flow of its collisions as compared to \oooo{} collisions. Here we show results for charged particle multiplicity $dN_\text{ch}/d\eta$ (top left), mean transverse momentum $\langle p_T\rangle$ (top middle), relative fluctuations of transverse momentum $\delta p_T/\langle p_T\rangle$ (top right), elliptic flow $v_2\{2,|\Delta\eta|>1\}$ (bottom left), triangular flow $v_3\{2,|\Delta\eta|>1\}$ (bottom middle) and the Pearson correlation coefficient $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (bottom right)\@. In each panel, we show the \oooo{} and \nene{} results, as well as their ratio, using both PGCM and NLEFT as nuclear structure inputs. For $\rho(v_2\{2\}^2,\langle p_T\rangle)$ a difference is taken instead of a ratio in the lower panel. We show statistical uncertainties (error bars), the total systematic uncertainty (solid bands) as well as its components being \emph{Trajectum} (hatched) and nuclear structure (dotted)\@. |
 | The deformed shape of $^{20}$Ne impacts the hydrodynamic flow of its collisions as compared to \oooo{} collisions. Here we show results for charged particle multiplicity $dN_\text{ch}/d\eta$ (top left), mean transverse momentum $\langle p_T\rangle$ (top middle), relative fluctuations of transverse momentum $\delta p_T/\langle p_T\rangle$ (top right), elliptic flow $v_2\{2,|\Delta\eta|>1\}$ (bottom left), triangular flow $v_3\{2,|\Delta\eta|>1\}$ (bottom middle) and the Pearson correlation coefficient $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (bottom right)\@. In each panel, we show the \oooo{} and \nene{} results, as well as their ratio, using both PGCM and NLEFT as nuclear structure inputs. For $\rho(v_2\{2\}^2,\langle p_T\rangle)$ a difference is taken instead of a ratio in the lower panel. We show statistical uncertainties (error bars), the total systematic uncertainty (solid bands) as well as its components being \emph{Trajectum} (hatched) and nuclear structure (dotted)\@. |
 | The deformed shape of $^{20}$Ne impacts the hydrodynamic flow of its collisions as compared to \oooo{} collisions. Here we show results for charged particle multiplicity $dN_\text{ch}/d\eta$ (top left), mean transverse momentum $\langle p_T\rangle$ (top middle), relative fluctuations of transverse momentum $\delta p_T/\langle p_T\rangle$ (top right), elliptic flow $v_2\{2,|\Delta\eta|>1\}$ (bottom left), triangular flow $v_3\{2,|\Delta\eta|>1\}$ (bottom middle) and the Pearson correlation coefficient $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (bottom right)\@. In each panel, we show the \oooo{} and \nene{} results, as well as their ratio, using both PGCM and NLEFT as nuclear structure inputs. For $\rho(v_2\{2\}^2,\langle p_T\rangle)$ a difference is taken instead of a ratio in the lower panel. We show statistical uncertainties (error bars), the total systematic uncertainty (solid bands) as well as its components being \emph{Trajectum} (hatched) and nuclear structure (dotted)\@. |
 | The deformed shape of $^{20}$Ne impacts the hydrodynamic flow of its collisions as compared to \oooo{} collisions. Here we show results for charged particle multiplicity $dN_\text{ch}/d\eta$ (top left), mean transverse momentum $\langle p_T\rangle$ (top middle), relative fluctuations of transverse momentum $\delta p_T/\langle p_T\rangle$ (top right), elliptic flow $v_2\{2,|\Delta\eta|>1\}$ (bottom left), triangular flow $v_3\{2,|\Delta\eta|>1\}$ (bottom middle) and the Pearson correlation coefficient $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (bottom right)\@. In each panel, we show the \oooo{} and \nene{} results, as well as their ratio, using both PGCM and NLEFT as nuclear structure inputs. For $\rho(v_2\{2\}^2,\langle p_T\rangle)$ a difference is taken instead of a ratio in the lower panel. We show statistical uncertainties (error bars), the total systematic uncertainty (solid bands) as well as its components being \emph{Trajectum} (hatched) and nuclear structure (dotted)\@. |
 | Point-nucleon densities of $^{16}$O (top) and $^{20}$Ne (bottom) obtained from NLEFT\@. The panels on the left show densities obtained from configurations aligned as described in the text, whereas the panels on the right show baseline densities obtained from configurations of which the angular information for each nucleon was randomized before the alignment of the nucleus. The background plots show slices of the densities through the origin. |
 | Point-nucleon densities of $^{16}$O (top) and $^{20}$Ne (bottom) obtained from NLEFT\@. The panels on the left show densities obtained from configurations aligned as described in the text, whereas the panels on the right show baseline densities obtained from configurations of which the angular information for each nucleon was randomized before the alignment of the nucleus. The background plots show slices of the densities through the origin. |
 | Point-nucleon densities of $^{16}$O (top) and $^{20}$Ne (bottom) obtained from NLEFT\@. The panels on the left show densities obtained from configurations aligned as described in the text, whereas the panels on the right show baseline densities obtained from configurations of which the angular information for each nucleon was randomized before the alignment of the nucleus. The background plots show slices of the densities through the origin. |
 | Point-nucleon densities of $^{16}$O (top) and $^{20}$Ne (bottom) obtained from NLEFT\@. The panels on the left show densities obtained from configurations aligned as described in the text, whereas the panels on the right show baseline densities obtained from configurations of which the angular information for each nucleon was randomized before the alignment of the nucleus. The background plots show slices of the densities through the origin. |
 | We show radial density profiles of $^{16}$O (left) and $^{20}$Ne (right), for both NLEFT and PGCM\@. The PGCM results are computed using the density $\rho_{m,2}$ as given in the text, while the NLEFT results come from smeared lattice configurations with $d_\text{min} = 0.5$\,fm. |
 | We show radial density profiles of $^{16}$O (left) and $^{20}$Ne (right), for both NLEFT and PGCM\@. The PGCM results are computed using the density $\rho_{m,2}$ as given in the text, while the NLEFT results come from smeared lattice configurations with $d_\text{min} = 0.5$\,fm. |
 | We show $v_2\{2,|\Delta\eta|>1\}$ (left), $v_3\{2,|\Delta\eta|>1\}$ (middle) and $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (right), with kinematic cuts as used by CMS (left and middle) and ATLAS (right)\@. |
 | We show $v_2\{2,|\Delta\eta|>1\}$ (left), $v_3\{2,|\Delta\eta|>1\}$ (middle) and $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (right), with kinematic cuts as used by CMS (left and middle) and ATLAS (right)\@. |
 | We show $v_2\{2,|\Delta\eta|>1\}$ (left), $v_3\{2,|\Delta\eta|>1\}$ (middle) and $\rho(v_2\{2\}^2,\langle p_T\rangle)$ (right), with kinematic cuts as used by CMS (left and middle) and ATLAS (right)\@. |
 | We show $v_2\{2,\text{OC}\}$ for \oooo{} collisions, using NLEFT nuclear structure input. The gray curves represent 20 different parameter choices taken from a Bayesian analysis \cite{Giacalone:2023cet}\@. The blue curve is the mean of the gray curves, and the error bars shown on it represent the statistical uncertainty. The blue band represents the systematic uncertainty, and is constructed from the spread of the gray curves. |
 | We show both $v_2\{2,|\Delta\eta|>1\}$ and $v_2\{2,\text{OC}\}$ for \oooo{} (NLEFT) (top)\@. Also shown is the ratio $v_2\{2,|\Delta\eta|>1\}/v_2\{2,\text{OC}\}$ (bottom), which serves as the correction factor discussed in the text. It can be seen that the correction factor is small but significant. |
 | We show the same correction factor as in the bottom panel of Fig.~\ref{fig:obscorrectionplot}, but for the ratio \nene{}/\oooo{} (NLEFT)\@. We show both the correction for $v_2\{2,|\Delta\eta|>1\}$ and for $v_3\{2,|\Delta\eta|>1\}$\@. It can be seen that whereas the former is a relatively small correction, the latter can be as much as 20\%\@. |
 | We show $v_2\{2,\text{OC}\}$ for \oooo{} (NLEFT), using three different grid spacings for the hydrodynamic calculations. In addition, we show the extrapolation to zero grid spacing, where the error bars show statistical uncertainty, and the bands show systematic uncertainty. |
 | We show $v_2\{2,\text{OC}\}$ for \oooo{} (NLEFT), where we either take only configurations with positive weight, or all configurations. In the latter case, we propagate the weights through the entire computation. The resulting correction factor is shown in the bottom panel. |
 | We show $v_2\{2,\text{OC}\}$ for \oooo{} (NLEFT), where we resolve the ambiguity with both choices described in the text. The resulting correction factor is also shown in the bottom panel, where the error bars show statistical uncertainty, and the bands show systematic uncertainty. |
 | We show the radial profiles of $^{16}$O (left) and $^{20}$Ne (right) for PGCM, where we show both sampling methods discussed in the text, alongside the original densities these configurations were sampled from. |
 | We show the radial profiles of $^{16}$O (left) and $^{20}$Ne (right) for PGCM, where we show both sampling methods discussed in the text, alongside the original densities these configurations were sampled from. |
 | We show $v_2\{2,\text{OC}\}$ for \oooo{} (PGCM), where we either sample independently from the densities provided by PGCM, or we sample such that we enforce that each region (corresponding with an alpha cluster) contains exactly 4 nucleons. The resulting correction factor is shown in the bottom panel. |
 | We show $v_2\{2,\text{OC}\}$ for \oooo{} (PGCM), where we use either the density $\rho_{m,1}$ or $\rho_{m,2}$ as inputs to \emph{Trajectum}\@. The resulting correction factor is shown in the bottom panel. |